A significant portion of computational resources of embedded systems for visual detection is dedicated to feature extraction, and this severely affects the detection accuracy and processing performance of the system. To solve this problem, we propose a feature descriptor based on histograms of oriented gradients (HOG) consisting of simple linear algebra that can extract equivalent information to the conventional HOG feature descriptor at a low computational cost. In an evaluation, a leading-edge detection algorithm with this decomposed vector HOG (DV-HOG) achieved equivalent or better detection accuracy compared with conventional HOG feature descriptors. A hardware implementation of DV-HOG occupies approximately 14.2 times smaller cell area than that of a conventional HOG implementation.